Robustness of the EWMA Control Chart to Non-Normality

Abstract

Rational subgroups of size n = 1 are frequently encountered in process monitoring and control. The Shewhart control chart for individuals is often used in these situations. It is well-known that the in-control average run length (ARL) of this chart is 370.4 under the assumption that the observations are selected at random from a normal population. When the assumption of normality is violated, the ARL of the individuals control chart is adversely affected. We show that an exponentially weighted moving average (EWMA) control chart can be designed so that it is robust to the normality assumption, that is, so that the in-control ARL is reasonably close to the normal-theory value for both skewed and heavy-tailed symmetric non-normal distributions. The EWMA chart also performs quite well in detecting shifts in the process mean.

• Average Run Length
• Exponentially Weighted Moving Average Control Charts
• Individuals Control Charts

Additional information

Notes on contributors

Connie M. Borror

Dr. Borror is a Visiting Professor in the Department of Industrial Engineering. She is a Member of ASQ. Her email address is [email protected].

Douglas C. Montgomery

Dr. Montgomery is a Professor in the Department of Industrial Engineering. He is a Fellow of ASQ.

George C. Runger

Dr. Runger is an Associate Professor in the Department of Industrial Engineering. He is a Senior Member of ASQ.